On theories of random variables

By I. Yaacov. Israel Journal of Mathematics, 2009

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We study theories of spaces of random variables: first, we consider random variables with values in the interval [0, 1], then with values in an arbitrary metric structure, generalising Keisler’s randomisation of classical structures. We prove preservation and non-preservation results for model theoretic properties under this construction: The randomisation of a stable structure is stable. The randomisation of a simple unstable structure is not simple. The randomisation of a stable structure is stable. The randomisation of a simple unstable structure is not simple. We also prove that in the randomised structure, every type is a Lascar type.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/caee0c5f7afca2baae9b22327dbc410452403938